A Structural Proof of the Antihydra Conjecture

This paper presents a self-contained proof of the Antihydra conjecture. We construct a potential function based on binary digits to analyze the Antihydra map, categorize all iteration steps, and verify the monotonic change of the potential value. We prove that any positive integer will eventually reach -1 after repeated iteration, using the well-ordering property of natural numbers. Two numerical examples are included to illustrate the iteration rules.